As someone who does mathematics or uses it extensively in your day job or research, which books do you think taught you the most and why?<p>You may be someone who belong to a field related to mathematics like CS, economics, etc.
Professional mathematician (but in business, not academia). I hold a PhD in mathematical physics. Below the list of books that taught me the most. However, these books are often not directly related to my current work. Also, I don't think they will be useful for everyone, as some of them are strong specialized books. These books mostly taught me to <i>think</i> like a mathematician. One of the strongest skills I learned as a mathematician is to dive deep into a topic and learn almost everything that you can learn about it (going from 80% of knowledge to 99.9%). I "read" these books completely several times in my career.<p>* Atiyah, Macdonald - Introduction to Commutative Algebra.<p>* Bourbaki (in French).<p>* Gasper, Rahman - Basic Hypergeometric Functions.<p>* Hasti et al - Elements Of Statistical Learning.<p>* Rudin - Real & Complex Analysis.<p>* Thomas, Thomas - Elements of Information Theory.
Bit of a brain dump here. Serre's <i>Trees</i> was pretty relevant to my studies, though left quite a few gaps for the reader to fill in.<p>Meier's <i>Groups, Graphs and Trees</i> is much more accessible and visual. Strongly recommended!<p>Knuth's notes on how to write mathematics well [1] were very influential.<p>Munkres' <i>Topology</i> is a classic, but I think I leaned more on Hatcher's <i>Algebraic Topology</i> towards the end.<p>Drobot's <i>Formal Languages and Automata Theory</i> was a lot of fun to self-study.<p>The <i>Graduate Texts in Mathematics</i> series was always reliable in my experience.<p>[1]: <a href="https://www-cs-faculty.stanford.edu/~knuth/klr.html" rel="nofollow">https://www-cs-faculty.stanford.edu/~knuth/klr.html</a>
Statistics by Roger Purves, David Freedman, Robert Pisani<p>Introduction to Linear Algebra,
by Gilbert Strang<p>A lot of my learning was self study. These books were very helpful to me.
The Foundations of Mathematics - Ian Stewart.<p>I wouldn't say it taught me the most, but more like it opened the door so I could learn the most out of everything after it.
For me it was Apostol's Calculus Vol 1 and Vol 2.<p>I am searching for books in mathematics that teach both the how and the why, here: <a href="https://news.ycombinator.com/item?id=31650459" rel="nofollow">https://news.ycombinator.com/item?id=31650459</a><p>I hope to get some insightful answers soon.